\documentclass[aps,prl,preprint,groupedaddress]{revtex4}
%\usepackage{multicol}
\begin{document}

\title{Dispersion Relations}

\section{Ferromagnetic}
\subsection{Chain}
\begin{equation}
\pm 2 \: \mathrm{J S} \; (1 - \cos(x))
\label{eq:fmc}
\end{equation}

\subsection{Square}
\begin{equation}
\pm 4 \: \mathrm{J S} \; (2 - \cos(x) + \cos(y))
\label{eq:fmsq}
\end{equation}

\subsection{Simple Cube}
\begin{equation}
\pm 4 \; \mathrm{J S} \; (3 - \cos(x) - \cos(y) - \cos(z))
\label{eq:fmsc}
\end{equation}

\subsection{Face-Centered Cube}
\begin{equation}
\pm 8 \; \mathrm{J S} \; (3 - \cos(x) \cos(y) - \cos(x) \cos(z) - \cos(y) \cos(z))
\label{eq:fmfcc}
\end{equation}

\subsection{Body-Centered Cube}
\begin{equation}
\pm 16 \; \mathrm{J S} \; (1 - \cos(x) \cos(y) \cos(z))
\label{eq:fmbcc}
\end{equation}

\section{Antiferromagnetic}
\subsection{Chain}
\begin{equation}
\pm 2 \; \mathrm{J S} \; \sin(x)
\label{eq:afmc}
\end{equation}

\subsection{Square}
\begin{equation}
\pm 4 \; \mathrm{J S} \; \sqrt{(2 - \cos(x) - \cos(y)) (2 + \cos(x) + \cos(y))}
\label{eq:afmsq}
\end{equation}

\subsection{Simple Cube}
\begin{equation}
\pm 4 \; \mathrm{J S} \; \sqrt{(3 - \cos(x) - \cos(y) - \cos(z)) (3 + \cos(x) + \cos(y) + \cos(z))}
\label{eq:afmsc}
\end{equation}

\subsection{Face-Centered Cube}
\begin{equation}
\pm 8 \; \mathrm{J S} \; \sqrt{(3 - \cos(y)\cos(z) - \cos(x)(\cos(y)+\cos(z))) (3 + \cos(y)\cos(z) + \cos(x)(\cos(y) + \cos(z)))}
\label{eq:afmfcc}
\end{equation}

\subsection{Body-Centered Cube}
\begin{equation}
\pm 16 \; \mathrm{J S} \; \sqrt{1 - \cos^{2}(x) \cos^{2}(y) \cos^{2}(z)}
\label{eq:afmbcc}
\end{equation}


\begin{tabular}{|cc||} 															\hline \hline

Name									&			Formula 																																						\\		\hline
Ferromagnetic																																																		\\		\hline
%\multicolum{2}{|c|}{Ferromagnetic}																																							\\		\hline
Chain									&		$\pm 2 \: \mathrm{JS} \; (1 - \cos(x))$																								\\ 
Square								&		$\pm 4 \: \mathrm{JS} \; (2 - \cos(x) + \cos(y))$																			\\
Simplie Cube					&		$\pm 4 \; \mathrm{JS} \; (3 - \cos(x) - \cos(y) - \cos(z))$														\\
Face-Centered Cube		&		$\pm 8 \; \mathrm{JS} \; (3 - \cos(x) \cos(y) - \cos(x) \cos(z) - \cos(y) \cos(z))$		\\
Body-Centered Cube		&		$\pm 16 \; \mathrm{JS} \; (1 - \cos(x) \cos(y) \cos(z))$															\\		\hline

Antiferromagnetic																																																																					  \\\hline
Chain									&		$\pm 2 \; \mathrm{JS} \; \sin(x)$																																																	\\ 
Square								&		$\pm 4 \; \mathrm{JS} \; \sqrt{(2 - \cos(x) - \cos(y)) (2 + \cos(x) + \cos(y))}$																									\\
Simplie Cube					&		$\pm 4 \; \mathrm{JS} \; \sqrt{(3 - \cos(x) - \cos(y) - \cos(z)) (3 + \cos(x) + \cos(y) + \cos(z))}$															\\
Face-Centered Cube		&		$\pm 8 \; \mathrm{JS} \; \sqrt{(3 - \cos(y)\cos(z) - \cos(x)(\cos(y)+\cos(z))) (3 + \cos(y)\cos(z) + \cos(x)(\cos(y) + \cos(z)))}$\\
Body-Centered Cube		&		$\pm 16 \; \mathrm{JS} \; \sqrt{1 - \cos^{2}(x) \cos^{2}(y) \cos^{2}(z)}$																													\\
																																																																												 \\\hline\hline
\end{tabular}



\end{document}

